EP0557591B1 - Dispositif pour déterminer l'orientation relative d'un corps - Google Patents
Dispositif pour déterminer l'orientation relative d'un corps Download PDFInfo
- Publication number
- EP0557591B1 EP0557591B1 EP92120363A EP92120363A EP0557591B1 EP 0557591 B1 EP0557591 B1 EP 0557591B1 EP 92120363 A EP92120363 A EP 92120363A EP 92120363 A EP92120363 A EP 92120363A EP 0557591 B1 EP0557591 B1 EP 0557591B1
- Authority
- EP
- European Patent Office
- Prior art keywords
- orientation
- sensor unit
- sensor
- unit
- ors
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Lifetime
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Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/183—Compensation of inertial measurements, e.g. for temperature effects
- G01C21/188—Compensation of inertial measurements, e.g. for temperature effects for accumulated errors, e.g. by coupling inertial systems with absolute positioning systems
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
- G01C19/02—Rotary gyroscopes
- G01C19/42—Rotary gyroscopes for indicating rate of turn; for integrating rate of turn
Definitions
- the invention relates to a device for determining the relative orientation of a body with respect to a reference orientation, with a movable orientation sensor unit.
- an angle measuring device which has a sensor unit with a plurality of gyroscopes, the gyroscopes of which Axes are arranged at right angles to each other.
- the measuring device is arranged in a housing which has two plane-parallel outer surfaces.
- a computer unit is also provided, which processes the angular velocity signals from the sensor unit and supplies the angle between two planes to be measured.
- One of the plane-parallel levels of the sensor unit is placed on the first level to be measured, then the sensor unit is guided to the other levels to be measured; there the latter is contacted with the second plane-parallel plane of the sensor unit.
- the components of the angular rate of rotation of the sensor unit are measured by the corresponding gyroscope, and the computer unit calculates the angle between the planes to be measured and displays the result.
- US Pat. No. 3,731,543 describes a gyroscopic alignment system in which inertial sensors are used to determine an angular position of an aircraft part on the basis of rotary movements.
- a nut sensor with two gyro systems is provided, which is mounted along a reference line during a determination process.
- a daughter sensor with only one gyro system is attached to the aircraft part during the determination process, the angular position of which is to be determined in relation to the reference line.
- the system compares the angular movements of the aircraft on the one hand on the reference line and on the other hand on the aircraft part in order to recognize its incorrect alignment with respect to a parallel to the reference line.
- British Patent 1,299,822 describes a self-calibrating system for navigation instruments, in which two gyro systems are provided on a platform, one of which is rotated successively around 180 ° and 90 ° around its spin axis for calibration purposes, while the other only uses the gyro system a 90 ° swivel is made.
- the measured values recorded in the various swivel positions allow the determination of drift coefficients.
- the invention is intended to provide a device or a method for determining the relative orientation of a body, with which the determination is also possible if the body and the reference surface do not perform any angular movements during the determination process.
- the device according to the invention is suitable for carrying out a method with which the relative orientation of an assembly with respect to a reference orientation can be determined by means of inertial angular velocity sensors.
- the reference orientation can be given, for example, by a reference surface that is located on a reference body.
- the inertial angular velocity sensors are generally referred to as gyroscopes.
- the angular velocities of the reference body and those of an orientation sensor unit are measured, which are moved from the reference body to the body (here: assembly) which is to be measured.
- the relative orientation of the body with respect to the reference body is calculated from both measurement information.
- the system to be measured need not move during the measurement, but it may move; this applies to the reference body alone, the body to be measured and both together.
- geophysical variables such as B. the Earth's rotation rate is not taken into account, since only the relative orientation is calculated without referring to an earth-fixed coordinate system.
- Fig. 1 Basic structure of the device according to the invention.
- Fig. 2 Different phases of the measuring process.
- Fig. 3 Example of the orientation of the coordinate axes during calibration.
- Fig. 4 Basic circuit structures for determining sum and difference components from angular velocity drift components for the calibration of the device according to Fig. 1.
- Fig. 5 Representation of swivel axes of inertial angular velocity sensors for drift calibration.
- the inertial angular velocity sensor 1 serves as an orientation sensor unit, while the other angular velocity sensor 2 is provided for determining the reference orientation. Both supply angular velocity vectors (rotation rate vectors) to the computing unit 4.
- the reference sensor unit 2 is abbreviated below with RES and the orientation sensor unit 1 with ORS.
- the ORS and the RES can each be realized by a gyro unit with three gyro measuring axes (gyro triad), which are oriented in such a way that within the gyro unit the measuring axes are not parallel to each other and the three measuring axes of a gyro unit are not in one plane, but are preferably arranged orthogonally.
- the ORS and the RES are to be constructed mechanically in such a way that they can be mechanically coupled in a defined and sufficiently rigid manner to one another and to the body to be measured (e.g. using recording devices) and to a reference body (reference surface) (e.g. using an adapter).
- the task of the computing unit 4 is to calculate the relative orientation between the initial orientation of the ORS and its final orientation from the angular velocities (rotation rates) measured by the ORS and the RES, the initial orientation preferably with the orientation of the reference body and the final orientation with the orientation of the body to be measured match or are at least clearly assigned to the reference body and the body.
- a Cartesian coordinate system k_BGR is assigned to the final orientation according to the body to be measured or its receiving device, which has a fixed orientation with respect to the body (e.g. an assembly).
- a coordinate system k_REF is assigned to the initial orientation of the reference body or the reference surface.
- the metrological task now consists in determining the orientation of the coordinate system k_BGR in relation to the reference orientation.
- the orientation of a coordinate system in relation to another coordinate system can be described mathematically by different parameter sets. Euler angles, direction cosine matrices or quaternions (Mc Kern, "A study of transformation algorithms for use in a digital computer", Masters thesis, T-493, Massachusetts Institute of Technology; Cambridge, 1968) are common.
- the different parameters can be converted into each other.
- the quaternion representation is used here.
- the RES and ORS are theoretically assigned Cartesian coordinate systems k_RES and k_ORS, and the angular velocities measured by the RES and ORS are referred to as w_RES and w_ORS in relation to these coordinate systems.
- the solution of the quaterion differential equation (1) integrated by the computing unit during phase II describes the orientation of the Coordinate system of the body to be measured (assembly or holding device) in relation to the reference coordinate system in the form of a quaternion ⁇ q_ [BGR; REF]. It applies under the above conditions: where the letters BGR and REF stand for the body (assembly) or the reference body.
- k_RES q_ [RES; REF] (t0) . ⁇ k_REF . ⁇ q _ * [RES; REF] (t0)
- k_ORS q_ [ORS; RES] (t0) . ⁇ k_RES . ⁇ q _ * [ORS; RES] (t0) (phase I only)
- the quaternion differential equation according to (1) must be initialized with the quaternion q_ [ORS; REF] (t0) at time t0. This quaternion or the orientation described by it is of course known due to the structural conditions.
- a significant limitation of the accuracy of the measurement method described above is due to the constant rate of gyro drift during a measurement, especially the so-called "run to run" drift. This is the part of the gyro drift that occurs every time the gyro system is switched on, i.e. every time the gyro is rotated to a different extent, i.e. deviates from the average gyro drift and, in contrast to the average gyro drift, cannot be easily compensated for.
- the type of calibration proposed here can be e.g. Use on aircraft to calibrate INS systems (inertial navigation systems), provided that they are designed redundantly, and is also suitable for calibrating accelerometer biases, i.e. for calibrating the drift of accelerometers.
- d_ORS and d_RES represent the drift (drift increment) vectors of the ORS and RES, respectively.
- the reorientation can be achieved by rotating the coordinate systems k_RES and k_ORS against each other based on an origin orientation and calculating the difference or the sum of the measurement vectors (components) d_RES, d_ORS in defined orientations.
- the ORS and the RES are to be coupled in a mechanically rigid and sufficiently defined manner.
- FIG. 3 three orientations for the coordinate systems k_ORS and k_RES are given as examples.
- FIG. 3a shows the origin orientation, from which the reorientations according to FIGS. 3b and 3c are carried out, in order to carry out the required measurements in each case.
- orientation a oil orientation
- the coordinate systems k_ORS and k_RES are oriented parallel to each other. Since both systems are rigidly coupled to each other, the difference in the measured angular velocities results in the difference in the drift vectors d_RES - d_ORS.
- the x and z axes of the coordinate systems k_ORS and k_RES are each oriented anti-parallel to one another in the alignment according to FIG. 3b.
- the totals of the drift components are obtained by summing the measuring components x, z of the ORS and the RES d_RES (x) + d_ORS (x) or d_RES (z) + d_ORS (z).
- the y axes of the coordinate systems k_ORS and k_RES are oriented antiparallel to one another.
- the sum of the y measurement components of the ORS and the RES gives the sum of the y drift components d_RES (y) + d_RES (y).
- FIGS. 4a to 4c For the calculation of the components for the alignments according to FIG. 3, basic circuit diagrams are shown in FIGS. 4a to 4c.
- FIG. 4a belongs to the orientation a of FIG. 3, and FIGS. 4b, 4c correspondingly belong to the orientation b and c of FIG. 3.
- the summers in FIGS. 4b, 4c and the difference former in FIG. 4a are each one Downstream device 7 for averaging, which serve to suppress so-called "short-term” and "random walk” drift components. Of the fractions above the average drift, the "short-term" fractions are those that are still correlated, while the "random walk” drift fractions are no longer correlated.
- the averaging time of the averager 7 depends on the variance of the disturbance variables and on the permissible error in the drift calculation.
- a major advantage of this method is that the environmental dynamics w_ORS or w_RES are eliminated due to the difference formation.
- drift increments are calculated using the previously described method. Then the method shown in FIG. 4 for calculating the sum or difference drift vector components also applies correspondingly to time-discrete signal processing.
- the ORS and the RES according to FIG. 5 can be constructed.
- the RES 2 and the ORS 1 are each equipped with a swivel mechanism 13 which allows the respective rotary triad 12R or 12O to be swiveled by 180 ° about an axis 8 or 9 which is transverse to the coordinate z RES or y ORS .
- the respective position of the y and z coordinates corresponding to the origin orientation is shown, as indicated in FIG. 3a.
- the orientations b and c according to FIG. 3 can be achieved, in which the necessary measurements are carried out, the RES and the ORS remaining mechanically rigidly coupled to one another, as shown in FIG.
- the "run to run" drift can then be calibrated with these measured values.
- the method for calibrating accelerometers is to be used, these should be replaced in FIG. 5 by the gyro triad.
- the calibration method is a simple solution, for example in aircraft navigation systems.
- RES and the ORS can be constructed identically. This also facilitates use in redundant systems.
Claims (6)
- Installation pour déterminer l'orientation relative d'un corps (K) par rapport à une orientation de référence, comprenant les composants suivants :a) une unité d'orientation mobile (1) réalisée comme capteur de la vitesse angulaire, et qui conduit d'une orientation inertielle définie par rapport à l'orientation de référence à une orientation finale définie par rapport à l'orientation du corps (K),b) une unité de capteur de référence pour déterminer l'orientation de référence sous la forme d'un second capteur de vitesse angulaire inertielle (2) dont l'orientation est définie par rapport à l'orientation de référence et reste par rapport à celle-ci,c) une unité de calcul (4) recevant les valeurs de mesure des vitesses angulaires fournies par les capteurs de vitesses angulaires (1, 2) pour calculer l'orientation relative du corps (K),d) une unité de sortie pour les signaux correspondant au résultat du calcul,caractérisé en ce que l'unité d'orientation et l'unité de capteur de référence présentent chaque fois une unité gyroscopique à trois axes de mesure gyroscopique et l'unité de calcul (4) est prévue pour intégrer l'équation différentielle servant à décrire l'orientation de l'unité de capteur d'orientation (1) par rapport à l'unité de capteur de référence (2) pour les valeurs des vitesses angulaires mesurées par l'unité à capteur d'orientation et l'unité à capteur de référence aussi longtemps que l'unité à capteur d'orientation (1) est conduite par l'unité à capteur de référence (2) vers le corps (K) à mesurer.
- Installation selon la revendication 1, caractérisée en ce que l'unité à capteur d'orientation (1) est couplée rigidement directement ou indirectement de manière mécanique à l'unité de capteur de référence (2) et peut être pivotée de 180° de sa position d'origine autour de l'axe de pivotement (9) du capteur d'orientation, axe perpendiculaire à l'un de ses axes de mesure et qui se situe dans un plan avec un axe de pivotement (8) du capteur de référence autour duquel l'unité à capteur de référence (2) peut pivoter de 180° à partir de son orientation initiale, cet axe étant perpendiculaire à l'axe de pivotement (9) du capteur d'orientation et à l'un de ses axes de mesure.
- Procédé de calibrage d'une installation de mesure fournissant des valeurs de mesure se rapportant à des mouvements dans un système à inertie et qui sont entachées d'un décalage, comprenant une paire d'unités de capteurs (1, 2) ayant chaque fois au moins deux axes de mesure perpendiculaires l'un à l'autre, une unité de capteur (1) pouvant pivoter de 180° autour d'un axe de pivotement (9) par rapport à son orientation initiale, cet axe étant perpendiculaire à l'un des axes de mesure de cette unité de capteur (1) et cet axe est compris dans un plan avec l'axe de pivotement (8) appartenant à l'autre unité de capteur (2) et autour duquel cette autre unité de capteur (2) peut pivoter de 180° à partir de son orientation initiale, cet axe (8) étant perpendiculaire à l'axe de pivotement (9) de la première unité de capteur (1) ainsi qu'à l'un des axes de mesure de l'autre unité de capteur (2), les deux unités de capteur (1, 2) étant couplées rigidement, mécaniquement pendant le calibrage, caractérisé en ce qu'on effectue les étapes de procédé suivantes :a) dans une orientation initiale des unités de capteur (1, 2), les deux unités de capteur déterminent chaque fois un triplet de valeurs de mesure pour un vecteur de valeur de mesure, pour permettre de former un vecteur de différence (d-) à partir des deux triplets,b) on pivote seulement l'une des unités de capteur (2) de 180° autour d'un premier axe (8) puis les unités de capteur (1, 2) déterminent chaque fois deux des trois composantes de valeurs de mesure comme paires de composantes pour additionner ces deux paires de composantes et donner un vecteur somme,c) on pivote l'autre unité de capteur (1) de 180° autour d'un second axe (9), cet axe étant perpendiculaire au premier axe (8) et les unités de capteur déterminent chaque fois les troisièmes composantes de valeurs de mesure pour additionner ces deux troisièmes composantes de valeurs de mesure et former une somme,d) à partir des paires de composantes et des troisièmes composantes de valeurs de mesure on forme un vecteur somme (d+) comprenant les paires de composantes des composantes de valeurs de mesure antiparallèles, et qui avec le vecteur de différence (d-) pour les unités de capteur (1, 2) définit chaque fois un vecteur de dérive pour le calibrage.
- Procédé selon la revendication 3, caractérisé en ce qu'en formant les vecteurs de somme et de différence on forme une valeur moyenne.
- Procédé pour déterminer l'orientation relative d'un corps (k) par rapport à une orientation de référence à l'aide d'une unité de capteur d'orientation conduite à partir d'une surface de référence d'un corps de référence vers une surface à mesurer du corps, selon lequela) on prévoit une unité de capteur de référence réalisée comme l'unité de capteur d'orientation comme capteur de mesure d'angle à inertie,b) initialement, l'unité de capteur d'orientation et l'unité de capteur de référence sont reliées rigidement au corps de référence,c) on découple l'unité de capteur d'orientation par rapport à l'unité de capteur de référence et on la conduit au corps à mesurer (K) pendant que l'unité de capteur de référence reste reliée rigidement au corps de référence (R),d) l'unité de capteur d'orientation est couplée au corps (K) à mesurer,
caractérisé en ce quee) pendant que l'unité de capteur d'orientation est conduite à partir de la surface de référence du corps de référence vers la surface à mesurer du corps (K), on mesure les composantes de la vitesse de rotation angulaire de l'unité de capteur d'orientation et on traite avec une unité de calcul pour obtenir un résultat donnant l'angle compris entre la surface de référence et la surface à mesurer,f) dans l'unité de calcul (4) on démarre l'intégration de l'équation différentielle servant à décrire l'orientation de l'unité de capteur d'orientation par rapport à l'unité de capteur de référence, entre les étapes de procédé b) et c) ci-dessus et on la termine après l'étape de procédé d. - Procédé selon la revendication 5, caractérisé en ce qu'on mesure chaque fois trois composantes des vitesses de rotation angulaires par l'unité de capteur d'orientation ou l'unité de capteur de référence et ces composantes sont transmises à l'unité de calcul (4).
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
DE4205869 | 1992-02-26 | ||
DE4205869A DE4205869A1 (de) | 1992-02-26 | 1992-02-26 | Einrichtung zur bestimmung der relativen orientierung eines koerpers |
Publications (2)
Publication Number | Publication Date |
---|---|
EP0557591A1 EP0557591A1 (fr) | 1993-09-01 |
EP0557591B1 true EP0557591B1 (fr) | 1996-04-17 |
Family
ID=6452612
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
EP92120363A Expired - Lifetime EP0557591B1 (fr) | 1992-02-26 | 1992-11-28 | Dispositif pour déterminer l'orientation relative d'un corps |
Country Status (2)
Country | Link |
---|---|
EP (1) | EP0557591B1 (fr) |
DE (2) | DE4205869A1 (fr) |
Cited By (7)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US8888786B2 (en) | 2003-06-09 | 2014-11-18 | OrthAlign, Inc. | Surgical orientation device and method |
US8911447B2 (en) | 2008-07-24 | 2014-12-16 | OrthAlign, Inc. | Systems and methods for joint replacement |
US8974468B2 (en) | 2008-09-10 | 2015-03-10 | OrthAlign, Inc. | Hip surgery systems and methods |
US8974467B2 (en) | 2003-06-09 | 2015-03-10 | OrthAlign, Inc. | Surgical orientation system and method |
US9271756B2 (en) | 2009-07-24 | 2016-03-01 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9339226B2 (en) | 2010-01-21 | 2016-05-17 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9549742B2 (en) | 2012-05-18 | 2017-01-24 | OrthAlign, Inc. | Devices and methods for knee arthroplasty |
Families Citing this family (19)
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DE4205868A1 (de) * | 1992-02-26 | 1993-09-02 | Teldix Gmbh | Verfahren und einrichtung zum kalibrieren einer messeinrichtung |
DE29522352U1 (de) | 1995-12-12 | 2002-07-18 | Busch Dieter & Co Prueftech | Lagemeßsonde zum gegenseitigen Ausrichten von Körpern |
FR2758625B1 (fr) | 1997-01-17 | 1999-03-19 | Sofresud | Dispositif apte a determiner la direction d'une cible dans un repere predefini |
DE19750441C2 (de) * | 1997-11-14 | 2000-01-27 | Markus Becker | Vorrichtung zur Erfassung und Steuerung von Körperhaltungen zur therapeutischen Anwendung in sitzender Haltung |
DE19800901B4 (de) * | 1998-01-13 | 2013-11-28 | Prüftechnik Dieter Busch AG | Lagemeßsonde zum gegenseitigen Ausrichten von Körpern |
DE10115548C2 (de) * | 2001-03-28 | 2003-11-06 | Busch Dieter & Co Prueftech | Meßgerät zur Bestimmung der räumlichen Orientierung eines Körpers relativ zu einer Bezugsrichtung |
FR2824132B1 (fr) * | 2001-04-27 | 2007-07-13 | France Etat | Dispositif, et procede associe, apte a determiner la direction d'une cible |
DE60139881D1 (de) | 2001-11-13 | 2009-10-22 | Nokia Corp | Verfahren, Vorrichtung und System zur Kalibrierung von Winkelratenmesssensoren |
FR2852405B3 (fr) * | 2003-03-14 | 2005-06-03 | Dispositif et procede associe apte a determiner la direction d'une cible | |
US7065888B2 (en) | 2004-01-14 | 2006-06-27 | Aai Corporation | Gyroscopic system for boresighting equipment |
DE102004057933A1 (de) * | 2004-12-01 | 2006-06-08 | Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V. | Verfahren und eine Vorrichtung zum Navigieren und Positionieren eines Gegenstands relativ zu einem Patienten |
FR2924215B1 (fr) * | 2007-11-23 | 2010-01-01 | Thales Sa | Systeme comprenant deux instruments combines et procede d'alignement du systeme |
FR2930933B1 (fr) * | 2008-05-06 | 2010-08-27 | Airbus France | Procede d'harmonisation d'au moins deux equipements d'un aeronef |
US10869771B2 (en) | 2009-07-24 | 2020-12-22 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9649160B2 (en) | 2012-08-14 | 2017-05-16 | OrthAlign, Inc. | Hip replacement navigation system and method |
US10363149B2 (en) | 2015-02-20 | 2019-07-30 | OrthAlign, Inc. | Hip replacement navigation system and method |
IL237971A (en) | 2015-03-26 | 2016-10-31 | Gandelsman Mark | A device and method for determining relative orientation between two different locations |
CA3056382A1 (fr) | 2017-03-14 | 2018-09-20 | OrthAlign, Inc. | Systemes et procedes de guidage pour un remplacement de hanche |
JP7344122B2 (ja) | 2017-03-14 | 2023-09-13 | オースアライン・インコーポレイテッド | 軟部組織の測定およびバランシングを行うシステムおよび方法 |
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-
1992
- 1992-02-26 DE DE4205869A patent/DE4205869A1/de not_active Ceased
- 1992-11-28 DE DE59206052T patent/DE59206052D1/de not_active Expired - Fee Related
- 1992-11-28 EP EP92120363A patent/EP0557591B1/fr not_active Expired - Lifetime
Cited By (10)
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US8888786B2 (en) | 2003-06-09 | 2014-11-18 | OrthAlign, Inc. | Surgical orientation device and method |
US8974467B2 (en) | 2003-06-09 | 2015-03-10 | OrthAlign, Inc. | Surgical orientation system and method |
US8911447B2 (en) | 2008-07-24 | 2014-12-16 | OrthAlign, Inc. | Systems and methods for joint replacement |
US8998910B2 (en) | 2008-07-24 | 2015-04-07 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9192392B2 (en) | 2008-07-24 | 2015-11-24 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9572586B2 (en) | 2008-07-24 | 2017-02-21 | OrthAlign, Inc. | Systems and methods for joint replacement |
US8974468B2 (en) | 2008-09-10 | 2015-03-10 | OrthAlign, Inc. | Hip surgery systems and methods |
US9271756B2 (en) | 2009-07-24 | 2016-03-01 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9339226B2 (en) | 2010-01-21 | 2016-05-17 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9549742B2 (en) | 2012-05-18 | 2017-01-24 | OrthAlign, Inc. | Devices and methods for knee arthroplasty |
Also Published As
Publication number | Publication date |
---|---|
EP0557591A1 (fr) | 1993-09-01 |
DE4205869A1 (de) | 1993-09-02 |
DE59206052D1 (de) | 1996-05-23 |
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